In my first year (summer) of undergraduate study, I was lucky enough to get a lab position with one of my professors. His research is primarily in spectral hole burning. Essentially he tasked me with taking an old broken spectrometer and get it into working order. He asked me to solder the severed engine control cables, the retrofit a new slit onto the spectrometer (design a part, have it made and delivered to the university), research and buy a lamp with appropriate power and and then couple the lamp (using the best method) to the spectrometer. I was to then optimize and calibrate the system (swap out the generic lenses, buy coated lenses w/ different focal lengths) and to make sure the output (fiber, open beam) was appropriate/high enough to be used in spectral hole burning experiments.

As stupid as this sounds, can I include this when applying? I keep reading about other people's research and I feel this may be "below" that.

I have something similar to this which culminated in an internal conference and poster presentation. It was lots of fiddling with a focused laser beam set-up and using it to thermally ablate material, and then investigate its electrical properties and do other characterisation methods. However, there's no publication to speak of as it remains an unsolved work.

I understand I should write it, but how should I go about writing such experiences?

I would list it under "experience" or "research" or whatever your heading is. I'd put something like "lab assistant" as the position (unless you have an official title). Then I would describe what you did below that, just like you did here.